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Mr Abbott said if elected, he would set up a judicial inquiry into allegations Ms Gillard acted improperly during her time as a lawyer with Slater and Gordon in the 1990s.

But he said the current government should act now to set up such an inquiry, on grounds the public could not wait up to 12 months for the next federal election.

Mr Abbott made the pledge, but refused to directly allege any criminal activity by Ms Gillard approving a re-election fund for union officials in 1992.

"Now, let's have the inquiry. Let's have it now. Let's get to bottom of these things and if the Prime Minister has nothing to hide, she won't run scared from this inquiry," he said.

Liberal heavyweight Senator George Brandis called a press conference on the matter on Friday, but he also was not prepared to directly allege Ms Gillard did act in a criminal manner, despite making a statement to that effect under parliament privilege in the Senate on Thursday.

Instead, Mr Brandis said it appeared to him and the Coalition, Ms Gillard may have breached criminal and commercial laws in helping to incorporate the fund - but he could not provide any evidence to guarantee his inherent allegation.

The Coalition has for months been alleging improper behaviour on the Prime Minister's part during her time as a lawyer, when she acted for her former boyfriend Bruce Wilson and his Australian Worker's Union colleague Ralph Blewitt.

Ms Gillard has repeatedly denied she was involved in any wrongdoing.

The Coalition has so far failed to provide any definitive evidence Ms Gillard knew she was involved in any wrongdoing at the time.